WASHINGTON (CNN) -- The top U.S. general in Iraq is recommending nearly 8,000 troop cuts in Iraq because of the improving situation there, a source close to the process has told CNN.

President Bush is considering Gen. David Petraeus' recommendation, which the official said is for a reduction of "well over 7,500 personnel," with the number including combat and support troops.

Some units would leave Iraq over the next five months as they complete their missions. But the first possible significant reduction -- an army brigade combat team -- would leave without replacement early next year, said the official, and that would free a brigade to be rotated to Afghanistan instead of Iraq.

Petraeus gave his recommendation to Defense Secretary Robert Gates and Joint Chiefs Chairman Adm. Mike Mullen, who have passed it and other recommendations along to the president.

A reduction in U.S. troops in Iraq would free up personnel for deployment to Afghanistan, a move urged by many commanders. The Taliban has stepped up its fight in that country, posing a challenge for the 33,000 U.S. troops deployed there.

The White House will not comment on the details of the Iraq recommendations. Spokeswoman Dana Perino said only that Bush "has received the assessment and recommendation from the Pentagon and he is considering his options."

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The president is expected to make an announcement on troop levels next week, the same time Gates and Mullen are to testify before the House Armed Services Committee about Iraq and Afghanistan.

There are 146,000 U.S. troops in Iraq.

Iraq and the United States are working to seal a security agreement that would set down a framework to withdraw troops.

In deciding on troop cuts, officials must weigh the need for sufficient U.S. military presence to help Iraq build its army and the significant sentiment there for U.S. and coalition troops to withdraw swiftly.

U.S. and Iraqi negotiators have been looking at a proposal calling for a complete U.S. military withdrawal by the end of 2011, and a deadline of June 30, 2009, to end the presence of U.S. troops in cities and towns.

Pentagon spokesman Geoff Morrell confirmed that Gates and Mullen made their recommendations to Bush on Wednesday, but gave no details.

"I can tell you that all these leaders are fundamentally in agreement on how we should proceed in Iraq," he said of Gates, Mullen, Petraeus, the Joint Chiefs of Staff and acting Central Command chief Gen. Martin Dempsey.

"Of course, now it is up to the commander-in-chief to decide the way ahead," Morrell said.

Officials said senior military leaders agree that the soonest troop levels could be significantly reduced would be early in 2009, when a 3,500-strong brigade from the 10th Mountain Division is scheduled to deploy to Iraq to replace a brigade leaving in mid-January.

Pentagon officials say that would free another brigade combat team to arrive in Afghanistan in mid-February.

The Army has identified units that could be available for Afghanistan, but it would take two to three months from the time the decision is made to assemble all the weaponry and equipment they need and ship them and the troops to Afghanistan, two Army officials told CNN.

The officials said the troops would not need extensive additional training to switch from Iraq to Afghanistan, especially those earmarked to train Afghan forces.

The increase in fighting in Afghanistan contrasts with the dramatic drop in violence across Iraq, where U.S. military is confident that it will continue to make strides.

The military transferred security control to Iraqis this week in the country's Anbar province, a Sunni Arab region once dominated by insurgents and now a bastion of the Awakening Councils, or Sons of Iraq, U.S.-backed groups that help with some security duties.

The military said it plans to transfer management of the Awakening Councils to the Iraqi government next month.

"The government of Iraq and coalition forces have agreed in principle to transfer all 100,000 Sons of Iraq," Maj. John Hall told CNN. "The transfer will start with the Baghdad province, with the other provinces following at a later date."

Under the security agreement still being negotiated, the Iraqi government could ask Americans to extend the tentative deadlines if it sees the necessity of doing so. A joint Iraqi-U.S. committee would then help define the duration and number of forces that would be needed and regularly assess the security situation on the ground.